Physics-
General
Easy

Question

A block(B) is attached to two unstretched springs S subscript 1 end subscript a n d blank S subscript 2 end subscript with springs constants k blank a n d blank 4 k commarepresentively (see Fig. I) The other ends are attached to identical supports M subscript 1 end subscript and M subscript 2 end subscript not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall I by small distance x left parenthesis F i g blank I I right parenthesis and released. The block returns and moves a maximum distance y towards wall 2.Displacements x blank a n d blank y are measured with respect to the equilibrium position of the block B The ratio fraction numerator y over denominator x end fraction is

  1. 4    
  2. 2    
  3. fraction numerator 1 over denominator 2 end fraction    
  4. fraction numerator 1 over denominator 4 end fraction    

The correct answer is: fraction numerator 1 over denominator 2 end fraction


    From energy conservation,
    fraction numerator 1 over denominator 2 end fraction k x to the power of 2 end exponent equals fraction numerator 1 over denominator 2 end fraction open parentheses 4 k close parentheses y to the power of 2 end exponent
    fraction numerator y over denominator x end fraction equals fraction numerator 1 over denominator 2 end fraction

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